Toyota Repair: Starting issues, fuel injection service, fuel injection system

Question
QUESTION: Hi Ted...this is actually a question regarding my 1999 Lexus es300 (no experts in that category so I thought I'd ask you, please help if you can).  Car has 106,000 miles very good condition...never had issues.  Recently while making a few short stops around the resort I work at, the car did not want to start after the 3rd stop (a couple hundred yards between on/off).  The car eventually started after a few minutes, and in reaction I had all new plugs, wires, and the fuel injection system cleaned.  However, it just repeated the same malfunction... I started the car (starts right up) drove it a few hundred yards, turned it off, dropped off some paper work 2-3 minutes< went out to the car and it did not want to start...on the 3rd try it started...usually this is turn the key and it starts immediately...what's up?

ANSWER: Does the engine turn over but not fire up or do you just hear a clicking noise without the engine turning over.?

---------- FOLLOW-UP ----------

QUESTION: OK, we're talking a cold engine...initially, it will start right up....no problem...when I drive it a couple hundred yards and then turn it off to drop off paperwork...when I try to re-start, it doesn't want to fire...it cranks and cranks.  If I wait a few minutes....It takes right off again.  Doesn't seem to do it once the engine is warmed up...just had all new plugs (NPK) and wires and the fuel ignition cleaned and the PCV valve replaced... the car idles fine, accelerates fine, turns off when I shut it off (so it's not a timing issue)...but it did just repeat the same issue after all this work was done...I'm miffed

Answer
Thanks for the reply, does the check engine light stay on when driving?
Do you know if they cleaned the inside of the throttle body when they did the fuel injection service? By cleaning the throttle body I mean actually cleaning the inside using carbon remover and a brush to clean all the carbon deposits out. Sometimres this condition can also be caused by a sticking idle air control valve (IAC) valve, it should be either cleaned or replaced while the throttle body is off.